You can SUP surf anywhere within the 'city' of San Clemente. The state park beaches which are Doheny SB, San Clemente SB, and San Onofre SB have specific rules regarding surfing with a paddle in your hands. Doheny, south of the hammer is OK. San Clemente State Beach (Calafia and south) No SUP. San O, from Dog Patch and south is OK. There are a few little gaps of enforcement at some specific breaks. Paddle out at North Beach and head south. You'll find various breaks all the way to about a mile south of the pier. As Josh said, watch the hidden rocks from south of North Beach to the pier. It's worth a walk down the beach or beach trail through that section at low tide to see where the rocks are.